circular (trigonometric) functions

hi, i need help solving this trigonometric equation:
sinx+3cosx=0
i don't know what to do as i can't just diviide the two to create tanx which is what i have been doing in previous questions...

yes, you are on the right track

sinx = -3cosx
sinx/cosx = -3
tanx = -3

so x must be in the II and IV quadrant by the CAST rule
take arctan(+3) to get 71.56º

then x=180º-71.56 = 108.44º
or
x = 360-71.56 = 288.44º

check them with a calculuator, they both work

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asked by elle

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